Solve for $x$ : $ 7|x - 2| + 7 = -2|x - 2| + 2 $
Add $ {2|x - 2|} $ to both sides: $ \begin{eqnarray} 7|x - 2| + 7 &=& -2|x - 2| + 2 \\ \\ { + 2|x - 2|} && { + 2|x - 2|} \\ \\ 9|x - 2| + 7 &=& 2 \end{eqnarray} $ Subtract ${7}$ from both sides: $ \begin{eqnarray} 9|x - 2| + 7 &=& 2 \\ \\ { - 7} &=& { - 7} \\ \\ 9|x - 2| &=& -5 \end{eqnarray} $ Divide both sides by ${9}$ $ \dfrac{9|x - 2|} {{9}} = \dfrac{-5} {{9}} $ Simplify: $ |x - 2| = -\dfrac{5}{9}$ The absolute value cannot be negative. Therefore, there is no solution.